This is an M-type system. Let's take Trappist 1 as an example star (0.0898 Mass of the Sun) and Trappist 1e as an example planet (0.772 mass of the earth, approx 0.029 AU from the star). Assume for now that none of the other Trappist rocky planets exist.
Now put a gas giant equivalent in size and mass to Jupiter as the outer planet of the system. I know gas giants are extremely unlikely in m-type systems, but stranger things have happened in the universe.
How close could the gas giant orbit the star without destabilizing 1e's orbit or turning it into a moon of the gas giant?